You'll start off by creating your first computer from stone, a glass pane and a single piece of redstone. ComputerCraft's machines use a lightweight programming language called Lua, which is relatively easy as programming languages go, and the ComputerCraft wiki can help you with recipes and introductory programs.
These computers are just the beginning. You can also build Turtles, which are small, self-propelled robots that can be programmed to perform tasks like placing or breaking blocks, though if you'd rather use your new creations for evil, you can attach a sword or an axe to the front of one and teach it how to kill.
Of course, you'll have to program your Turtles, and while the newbie programmer might do this one machine at a time, seasoned developers know that ComputerCraft will let them build wireless modems which can transfer data between a computer and a whole army of Turtles. That said, they're affected by the weather and electrical storms will reduce their effectiveness.
I'm sure you're already coming up with ideas about what kind of programs you can write and how you can make best (or worst) use of a detachment of unquestioning, unfeeling slaves. Like Minecraft itself, ComputerCraft provides a canvas for your creativity and a toy within a toy. There's all sorts you can do just within the basic computers provided by this mod (which have just received colour support), so there's nothing to stop you from, for example, programming your own games within this game.
In case you missed the link above, ComputerCraft is right here and you'll need to grab Minecraft Forge too. I expect I'll be hearing your stories of death beneath the wheels of malfunctioning android armies by the end of the the week.
As a postscript, the mod's Cambridge-based creator, Dan200, is hoping to speak about ComputerCraft at this year's MineCon. Here's his pitch, and good luck to the fine fellow.